In some wireless networks, long term evolution (LTE) networks being one example, user equipment (UE) obtains uplink synchronization by transmitting a preamble to a base station (or evolved Node B, eNB) via a physical random access channel (PRACH). The preambles used in the PRACH are constant-amplitude Zadoff-Chu (ZC) sequences of a prime length, such that the cyclic auto-correlation of the ZC sequence is an ideal delta function and the cyclic cross-correlation of two ZC sequences with different root sequence indices is a constant of magnitude
      1                  N        ZC              ,where NZC is the ZC sequence length. At the base station, network resources are allocated responsive to preamble detection.